We prove an estimate on denominators of rational Drinfeld asso- ciators. To obtain this result, we prove the corresponding estimate for the p-adic associators stable under the action of suitable elements of Gal(¯Q/Q). As an application, we settle in the positive Duflo's question on the Kashiwara– Vergne factorizations of the Jacobson element Jp(x, y) = (x + y)p − xp − yp in the free Lie algebra over a field of characteristic p. Another application is a new estimate on denominators of the Kontsevich knot invariant.